I shoot right handed but have a dominant left eye. I keep my left eye closed, and it works. I tried training myself to shoot with both eyes open, and if i start with the left closed and slowly open, it seems to work. On more than one occasion though, i have completely missed my target and buried my arrow into the wood frame holding it when shooting with both eyes open, so i wouldnt trust myself in a hunting situation. Since you cant keep your eye closed, i have heard of a "fix" but havent tried it myself yet. Try taping a piece of cardboard to the bill of your hat so it hangs down and blocks the vision of your left eye. I think they even sell a gizmo commercially for this. that way you can keep both eyes open and not have to wear a patch. maybe you can even rig it so you can flip it down when you need to.